a. \(1-2y+y^2=\left(1-y\right)^2\)
b. \(\left(x+1\right)^2-25=\left(x+1+5\right)\left(x+1-5\right)=\left(x+6\right)\left(x-4\right)\)
c. \(1-4x^2=\left(1+2x\right)\left(1-2x\right)\)
d. \(8-27x^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
e. \(27+27x+9x^2+x^3=\left(x+3\right)^3\)
f, \(8x^3-12x^2y+6xy^2-y^3=\left(2x-y\right)^3\)
g, \(x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
\(\left(a\right)1-2y+y^2\)
\(\Leftrightarrow y^2-2y+1\)
\(\Leftrightarrow\left(y-1\right)^2\)
\(\left(b\right)\left(x+1\right)^2-25\)
\(\Leftrightarrow\left(x+1\right)^2-5^2\)
\(\Leftrightarrow\left(x-4\right)\left(x+6\right)\)
\(\left(c\right)1-4x^2\)
\(\Leftrightarrow1-\left(2x\right)^2\)
\(\Leftrightarrow\left(1-2x\right)\left(1+2x\right)\)
\(\left(d\right)8-27x^3\)
\(\Leftrightarrow2^3-\left(3x\right)^3\)
\(\Leftrightarrow\left(2-3x\right)\left(4+6x+9x^2\right)\)
\(\left(e\right)27+27x+9x^2+x^3\)
\(\Leftrightarrow\left(x+3\right)^3\)
\(\left(f\right)8x^3-12x^2y+6xy^2-y^3\)
\(\Leftrightarrow\left(2x\right)^3-12x^2y+6xy^2-y^3\)
\(\Leftrightarrow\left(2x-y\right)^3\)
\(\left(g\right)x^3+8y^3\)
\(\Leftrightarrow\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
a) 1 - 2y + y2
=> (1-y)
b) ( x + 1 )2 - 25
=>(x+1-5)(x+1+5)
=>(x-4)(x+6)
c) 1 - 4x2
=>12-22x2
=>12(2x)2
=>(1-2x)(1+2x)
d) 8 - 27x3
=>23-33x3
=>23(3x)3
=>(2-3x)[22+2.3x+(3x)2]
=>(2-3x)(4+6x+9x2)
e) 27 + 27x + 9x2 + x3
=>(3+x)3
f) 8x3 - 12x2y + 6xy2 - y3
=>2x(4x26x+3)
g) x3 + 8y3
=>x3+(2y)3
=>(x+2y)[x2-x.2y+(2y)2]
=>(x+2y)(x2-2xy+4y2)
a,(1-y)\(^2\)
b,(x+1)\(^2\)-5\(^2\)
\(\Rightarrow\)(x+1-5)(x+1+5)
c,1\(^2\)-4x\(^2\)\(\Rightarrow\)(1-4x)(1+4x)
d,2\(^3\)-27x\(^3\)\(\Rightarrow\)(2-27x)(2\(^2\)+54x+27x\(^2\))
e,...
f,(x-y)\(^3\)
g,....